Accurate prediction of pile base resistance is essential for the safe and economical design of deep foundations, particularly in soft soils where load-transfer mechanisms are highly nonlinear and uncertain. This study develops a comparative, probabilistic, and interpretable machine learning framework for predicting pile unit base resistance using five input variables: applied load, settlement, effective pile length, axial stiffness, and SPT value. A Gaussian Process Regression model with an automatic relevance determination (ARD) Exponential kernel achieved the best performance, with RMSE = 262.11 kPa, R2 = 0.943 on an independent test set, and 95% prediction intervals with 96.46% coverage. Beyond record-level evaluation, a leave-one-pile-out validation (the first grouped validation applied to this database) showed harder generalization to entirely unseen piles, driven mainly by a per-pile level offset rather than shape mismatch (within-pile correlation = 0.975). A sequential next-stage scheme, calibrating this level from a pile’s early loading stages, then predicted its remaining segments with consistently strong agreement (Willmott’s d = 0.76–0.83), supporting practical extension of partial load tests. Interpretability was assessed using ARD, SHAP, permutation/ablation importance, and partial dependence/accumulated local effects analysis, identifying settlement as the dominant predictor. The framework combines accuracy, calibrated uncertainty, interpretability, and validated segment-level extrapolation for reliability-oriented pile assessment.
Predicting the critical buckling load of slender structural rods is essential for reliable and weight-efficient design of automotive steering and suspension linkages such as tie rods. This study evaluates the performance of four machine learning models such as artificial neural network (ANN), support vector regression (SVR), Gaussian process regression (GPR), and random forest (RF) in predicting the critical buckling load (Pcr) from geometric and material design parameters which are rod length (L), diameter (D), wall thickness (t), Young’s modulus (E), and initial geometric imperfection (δ₀). A dataset was generated using a parametric MATLAB code, and models were trained on an 80/20 train-test split with min-max normalized inputs. ANN and GPR achieved near-perfect predictive accuracy (R²=1.000), outperforming SVR and RF (R² = 0.92-0.96). Input sensitivity was assessed using permutation importance across all four models, complemented by Garson’s algorithm and the connection weight method. Rod length and diameter were consistently identified as the dominant parameters governing buckling resistance, jointly accounting for the majority of predictive importance; when length was held constant, diameter alone emerged as the leading parameter, followed by comparable contributions from wall thickness and Young’s modulus. Initial imperfection showed negligible influence according to all permutation-based methods, although the connection weight method disagreed sharply, illustrating a key limitation of weight-based sensitivity analysis relative to permutation-based approaches.
This study presents three advanced machine learning models: the evolutionary Gaussian process inference model, the artificial satellite search algorithm–moment balance machine (ASSA-MBM), and the Operation Rain Forest (ORF), which are designed to predict the maximum reinforcement load in geosynthetic-reinforced soil structures. These models were developed to enhance both predictive accuracy and model interpretability by incorporating state-of-the-art optimization algorithms and explainable machine learning frameworks. A comprehensive evaluation was conducted using 10-fold cross-validation, and the proposed models were benchmarked against previously developed AI models from literature, as well as traditional and semiempirical approaches such as Rankine, Coulomb, and K -stiffness. Among the proposed models, ASSA-MBM consistently achieved the best performance, recording the lowest testing root mean squared error (0.617), the highest correlation coefficient ( R = 0.918 ), and the highest reference index ( RI = 0.951 ). Additionally, the ORF model offers transparency by generating mathematical regression equations, which are crucial in geotechnical engineering.
The results confirm the accuracy, interpretability, and computational efficiency of the integrated FEA-ML approach as an alternative to traditional bearing capacity analysis.